Representative Joe Barton, Republican of Texas (Brendan Hoffman/Bloomberg News)

Rep. Joe Barton (R-Texas) wants the federal government to shut down the Internet — or at least, the parts of it that are being used by the Islamic State.

"They are really trying to use the Internet and all the social media to intimidate and beat us psychologically," Barton said during a House committee hearing Tuesday. "Isn't there something we can do to shut those Internet sites down?"

Barton conceded that censoring the Web sites might be difficult — "I know they pop up like weeds" — but plowed ahead with his proposal, suggesting that the Federal Communications Commission attempt to shut down the sites.

"They're using the Internet in an extremely offensive and inappropriate way against us," he continued.

Barton's proposal comes days after a series of deadly terrorist attacks in Paris and amid a political battle over whether to accept thousands of Syrian refugees into the United States. Intelligence officials have called for expanding the government's surveillance powers in the wake of the blasts, and Barton appeared to join them Tuesday when he suggested granting the government provisional authority to clamp down on ISIS-affiliated Internet media.

There's just one problem with Barton's plan: The Internet may be a little more complicated than he thinks.

The FCC doesn't have the authority to regulate individual Web sites, agency chairman Tom Wheeler replied. And the commission likely won't want even a temporary authority to censor the Web. Here's why.

Critics of the commission have complained that the FCC's net neutrality rules are simply a backdoor way for the agency to regulate the Internet. Even if it were technically feasible for the government to find and shut down every single ISIS Web site (it's not), for the FCC to do so would simply lend credence to those attacks. And it would undermine the spirit of the net neutrality rules, which are aimed at allowing all (legal) speech — for better or for worse — to flourish online without interference by anybody.

Congress could probably get around that by ruling ISIS-affiliated speech illegal. But then we'd have an even bigger First Amendment problem on our hands.

In a statement late Tuesday afternoon, Barton clarified that he was "in no way suggesting we shut down the Internet."

"I am very mindful of privacy and First Amendment issues on the Internet," Barton said, "and believe that Congress should have a robust discussion on ways to protect American lives, while preserving American rights."